This history of physics focuses on the question, "How do bodies act on one another across space?" The variety of answers illustrates the function of fundamental analogies or models in physics as well as the role of so-called unobservable entities. Forces and Fields presents an in-depth look at the science of ancient Greece, and it examines the influence of antique philosophy on seventeenth-century thought. Additional topics embrace many elements of modern physics--the empirical basis of quantum mechanics, wave-particle duality and the (...) uncertainty principle, and the action-at-a-distance theory of Wheeler and Feynman. 1961 ed. (shrink)

An in-depth look at the science of ancient Greece, this volume examines the influence of antique philosophy on 17th-century thought. Additional topics embrace many elements of modern physics: the empirical basis of quantum mechanics, wave-particle duality and the uncertainty principle, and the action-at-a-distance theory of Wheeler and Feynman. 1961 edition.

It is with sincere appreciation that I commend this edited collection to readers of the AJTP. The collection meets the task of promoting lively discussion that addresses the interface between theology and philosophy, especially as shaped by empiricist, naturalist, process, and pragmatist traditions. As the most recent volume in the series Toward Ecological Civilization, it delivers papers from the Tenth International Whitehead Conference and Ninth International Forum on Ecological Civilization, held in Claremont, California, June 2015, thereby delivering on a second (...) focus for the AJTP: the development of liberal religious thought in America.The authors gathered in this collection take seriously the earnest and... (shrink)

ABSTRACT This article examines the resonance of Robert Owen’s ideas in the field of women’s rights with the view to determining the extent of their dissemination in transnational networks. The article focuses on the life and work of Anna Doyle Wheeler, which offers an important, though understudied, case for exploring early feminist circles, and, as she was a friend of Owen’s and one of his earliest supporters from the 1820s onwards, the impact of Owen’s ideas within these circles. The (...) article traces Wheeler’s discovery of Owen’s system and examines how Wheeler fused Owen’s co-operative ideals with calls for women’s emancipation. It analyses her famous Appeal of One Half of the Human Race (1825), a work that urged women to engage ardently in the battle for their political and civil rights, and to join in the establishment of co-operative communities. The article concludes by examining how Wheeler attempted to articulate and put into practice these political and co-operative principles through her involvement in the English, French and Irish co-operative movements, and through her association with Désirée Véret and the contributors to the Tribune des femmes. (shrink)

The rule books, though they claimed to heed only the call of logic, were nonetheless bound by their historical context: punctuation guidelines have been heavily indebted to intellectual, cultural, and aesthetic trends. No matter what analytical authority rule books claimed, their codifications had at least as much to do with their historical context as with syntax. When punctuation is properly contextualized, it can yield insight into problems that transcend disciplinary boundaries: it asks us to consider how we communicate within the (...) disciplines and beyond them and how disciplines create and maintain interpretive norms. It is this account of punctuation that I begin to develop here.I want to track the much-maligned semicolon and its fellow punctuation marks as rules for their usage were established and evolved. I consider the consequences of the nineteenth-century explosion of systems of grammar rules by way of the story of a semicolon in a statute that deprived Bostonians of late-night liquor from 1900–1906. The “Semicolon Law,” as it came to be known, exemplifies problems of interpretation still live in legal theory. I contrast the demands of legal formalism with the expectations of close reading in the humanities and social sciences. I conclude by attending to the inheritance left to us by nineteenth-century grammarians' impassioned attempts to bring order to English: The Chicago Manual of Style. I raise some critical questions about our attitudes towards rules, and consider how those attitudes influence our approach to punctuation and our passions about semicolons. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Reviewed by:Religion within the Limits of History Alone: Pragmatic Historicism and the Future of Theology by Demian WheelerNancy FrankenberryReligion within the Limits of History Alone: Pragmatic Historicism and the Future of Theology. Demian Wheeler. Albany: SUNY Press, 2020. ix+511pp. $95.00 hardcover.The history of Christian theology since the Enlightenment has been a series of unsuccessful attempts to evade a stark dilemma: either fundamentalism or atheism. Contemporary liberal theologians have (...) argued that this dilemma is [End Page 97] entirely too stark, too eliminative of the creative possibilities of revisionism. Liberal theology has wanted to revise and reinterpret Christian faith in conformity with history, reason, a scientific worldview, and a sophisticated grasp of the significance of symbol, analogy, and metaphor in the lives of religious practitioners. Eliminating both supernaturalism and anthropomorphism, liberal theology would make Christianity more intellectually tenable, rescuing it from the literalist hands of fundamentalists, without collapsing it into the equally literalist arms of atheism.The extreme difficulty of evading the either-or dilemma of choosing either fundamentalism or atheism landed liberal theology in a catch-22: either it rejected the intellectually untenable elements of belief, in which case it eliminated just those beliefs that constituted its appeal to popular piety, or it retained certain supernaturalistic and anthropomorphic beliefs, understood as “symbolic,” in which case it forfeited intellectual intelligibility and any appeal to sophisticated moderns. The first version is far too weakened for ordinary American Christians, and the second is still too religious for the masters of suspicion and their followers.It is for this reason that the history of American religious thought reveals a grave irony that complicates the hopes of pragmatic historicists, the protagonists of this superbly clear and rich, deep dive into authors that most readers of this journal will have read, but perhaps not have synthesized as thoroughly as has Demian Wheeler. That irony, as Wheeler knows, is that the more intellectual changes pragmatic historicists make to traditional Christian belief, the more they help to make unbelief viable. The question then arises as to whether pragmatic historicism is simply a half-way house on the road to an atheistic destination. Or, if the word “atheism” sounds too old-fashioned, like something that went out with steamships and girdles, then “agnosticism.” Or, if “agnosticism” still smacks too much of stale debates, why not “pantheism,” as recently revived by Mary-Jane Rubenstein?The detailed development, the verbal bravura, and the measured knowledge in this book are astonishingly impressive. Wheeler’s initial thesis is that liberal theology, particularly of the early Chicago School, and American pragmatism, particularly C. S. Peirce, William James, and John Dewey, provide important resources for meeting the challenges posed by the rise of historical consciousness. Sheila Davaney has designated this tradition “pragmatic historicism,” and Wheeler aims to show its compelling import for the future of theology itself. A good deal of the book is devoted to exposition and defense of the views of: Ernst Troeltsch, James, Dewey, George Burman Foster, Shirley Jackson Case, Shailer Matthews, and Gerald Birney Smith, down to Delwin Brown, Sheila Davaney, and William Dean (Wheeler’s teachers at Iliff), along with Gordon [End Page 98] Kaufman and Sallie McFague. In the last chapter, Wheeler draws expertly on the theological views of Bernard Loomer, Michael Hogue, Donald Crosby, and Wesley Wildman. Such an all-star cast deserves to receive all the attention they can get. Wheeler’s occasional emendations come as glittering nuggets of constructive engagement. He does not simply call for a pragmatic historicist approach to theology, but he executes one as well, showing in more detail than his predecessors what it means for such topics as religious diversity (chapters 3 and 4), the nature of authority (chapter 5), the meaning of critical realism, fallibilism, and an altered correspondence theory of truth (chapters 6 and 7), and the doctrine of God (chapter 8). With the same exhaustive treatment that his doktorvater Gary Dorrien has devoted to liberal theology’s history and contemporary expressions, Wheeler carefully saves pragmatic historicism from relativism, expertly critiques all the leading theologians of the “inclusivist,” “exclusivist,” and “pluralist” theologies of religions, while arguing the superiority of his own “particularist” corrective to pluralistic... (shrink)

Two types of Judeo-Christian perspective stress the imperative to act to relieve suffering and transcend violence: liberation theology and the "religious humanitarian perspective." Both link ethics and action; both influence political debate.

Lynch addresses the return to Immanuel Kant—a "prophet of progressive international reform"—and examines the relationship between the Kantian system of ethics and the development of international law in the post-Cold War era.

Wrestling with God in the modern West -- Understanding Christian wrestling about ethics -- Wrestling with the violence of conquest -- Wrestling with war in a modern world -- Wrestling with the violence of oppression -- Wrestling with violence and injustice abroad and at home -- Has anyone prevailed?

On the basis of careful textual exegesis and philosophical analysis, and contrary to the received view, Mark R. Wheeler demonstrates that Aristotle presents and systematically explicates his definition of the essence of the truth in the Metaphysics. Aristotle states the nominal definitions of the terms "truth" and "falsehood" as part of his arguments in defense of the logical axioms. These nominal definitions express conceptions of truth and falsehood his philosophical opponents would have recognized and accepted in the context of (...) dialectical argument. On the basis of these nominal definitions, Aristotle develops his definitions of the essences of truth and falsehood--his "real" definitions of truth and falsehood. Aristotle's methodical exposition of his essential definitions of truth and falsehood in the Metaphysics serves as a well-developed example of how his philosophical inquiry starts with nominal definitions and ends with real definitions. Wheeler also argues for the novel claim that Aristotle defines the most fundamental kind of truth in terms of accurate measurement. Aristotle's metrical conception of truth serves as the theoretical basis for specifying the truth conditions of various assertions, for identifying the sorts of beings implicated in these truth conditions, and for explaining the nature of approximate truth and falsehood. Far from offering us a minimal account of truth, Wheeler shows how Aristotle offers us a sophisticated and metrical theory of truth. (shrink)

Coherentism maintains that coherent beliefs are more likely to be true than incoherent beliefs, and that coherent evidence provides more confirmation of a hypothesis when the evidence is made coherent by the explanation provided by that hypothesis. Although probabilistic models of credence ought to be well-suited to justifying such claims, negative results from Bayesian epistemology have suggested otherwise. In this essay we argue that the connection between coherence and confirmation should be understood as a relation mediated by the causal relationships (...) among the evidence and a hypothesis, and we offer a framework for doing so by fitting together probabilistic models of coherence, confirmation, and causation. We show that the causal structure among the evidence and hypothesis is sometimes enough to determine whether the coherence of the evidence boosts confirmation of the hypothesis, makes no difference to it, or even reduces it. We also show that, ceteris paribus, it is not the coherence of the evidence that boosts confirmation, but rather the ratio of the coherence of the evidence to the coherence of the evidence conditional on a hypothesis. (shrink)

Mark Richard Wheeler - Aristotle on Truth - Journal of the History of Philosophy 44:3 Journal of the History of Philosophy 44.3 469-470 Paolo Crivelli. Aristotle on Truth. Cambridge-New York: Cambridge University Press, 2004. Pp. xi + 340. Cloth, $85.00. A thorough contemporary study of Aristotle's theory of truth is welcome. Adopting a frankly analytic approach, Professor Crivelli addresses all of the most important Aristotelian texts on truth. He provides close and careful exegesis, attending to philological and interpretive difficulties (...) related to the manuscripts and alternative translations. In the spirit of Hintikka, Łukasiewicz, and Mignucci, the tools of contemporary logical analysis are applied effectively and yield rigorous restatements of Aristotle's.. (shrink)

Examines the philosophical, scientific, and theological aspects of the character of the human mind.

One approach to hypnosis suggests that for hypnotic experience to occur frontal lobe activity must be attenuated. For example, cold control theory posits that a lack of awareness of intentions is responsible for the experience of involuntariness and/or the subjective reality of hypnotic suggestions. The mid-dorso-lateral prefrontal cortex and the ACC are candidate regions for such awareness. Alcohol impairs frontal lobe executive function. This study examined whether alcohol affects hypnotisability. We administered 0.8 mg/kg of alcohol or a placebo to 32 (...) medium susceptible participants. They were subsequently hypnotised and given hypnotic suggestions. All participants believed they had received some alcohol. Participants in the alcohol condition were more susceptible to hypnotic suggestions than participants in the placebo condition. Impaired frontal lobe activity facilitates hypnotic responding, which supports theories postulating that attenuation of executive function facilitates hypnotic response, and contradicts theories postulating that hypnotic response involves enhanced inhibitory, attentional or other executive function. (shrink)

We examined the hypothesis that a tendency to experience the world in terms of a sense of ‘special’ connection is responsible for the self-transcendent value dimension identified by multi-dimensional scaling and constitutes a common factor for different religious and non-religious interpretations of spirituality. Eight different groups were studied including: six different types of faith leaders in India and the UK, people who self-rated as spiritual but not religious, and those self-rating as neither spiritual nor religious. They completed a questionnaire that (...) assessed the strength of their spirituality irrespective of type and the experience of special connection to the following categories: people, nature, places and the universe, with and without using the term spiritual. For all eight samples the different types of connection were highly inter-correlated, and self-perceived spirituality correlated with the sum of connection items irrespective of whether items included the term spiritual or not. Variation between groups in the size of the latter correlation was consistent with different interpretations of spirituality in those groups. Although the meaning of spirituality is socially constructed, variability within faith leader groups suggests that its interpretation is also affected by personality. (shrink)

Sample quotes from emails sent by visitors to Mary Klages's successful literary theory web pages on which this book is based: 'Finding your course was a godsend ...

Michael Tonry, Sentencing Matters (New York: Oxford University Press, 1996, 240pp.

In the Philippines, all transplant centers are mandated by the Department of Health (DOH) to have a Hospital Transplant Ethics Committee (HTEC) to ensure that donations are altruistic, voluntary and free of coercion/commercial transactions. This study was undertaken primarily to describe the organizational and functional profile of existing HTECs and identify areas for improvement. This is a descriptive cross‐sectional study. There was variation in their logistical arrangements (support from hospital, filing systems, office spaces), operations (length and frequency of meetings, number (...) of referrals) and membership (composition, qualifications, occupation, training). The approval rate for donor‐recipient pairs is high with the majority of cases made by living non‐related donors. Appropriate reasons were cited for rejection. The perception of HTECs is that they are competent and confident in their decision‐making. However, there is a need to standardize HTEC composition, provide operating procedures and additional training which can be done by the DOH. (shrink)

En quoi consiste, ou devrait consister, l'éthique professionnelle en enseignement? Comment se manifeste-t- elle dans les gestes pédagogiques? Selon quels critères peut-on la juger? Comment développer l'éthique professionnelle dans le cadre des formations initiale et continue en enseignement? En tenant compte du contexte social et culturel du Québec, des principes éthiques déjà énoncés par le ministère de l'Education ainsi que des lois, codes et conventions ayant des incidences sur la pratique enseignante, les auteures présentent des éléments à considérer pour la (...) réflexion éthique sur l'agir professionnel. Elles proposent des clarifications conceptuelles et un certain nombre de repères et de balises afin de guider les enseignants et de stimuler la discussion sur l'éthique professionnelle, non seulement dans la classe, mais aussi dans l'école et dans la société. (shrink)

Using a two-part instrument consisting of eight vignettes and twenty character traits, the study sampled 141 employees of a mid-west financial firm regarding their predispositions to prefer utilitarian or formalist forms of ethical reasoning. In contrast with earlier studies, we found that these respondents did not prefer utilitarian reasoning. Several other hypotheses were tested involving the relationship between people's preferences for certain types of solutions to issues and the forms of reasoning they use to arrive at those solutions; the nature (...) of the relationship between utilitarian and formalist categories ; and the possibility of measuring ethical predispositions using different methods. (shrink)

In lieu of an abstract, here is a brief excerpt of the content:Response to Masafumi Ogawa, “Music Teacher Education in Japan: Structure, Problems, and Perspectives”Peggy WheelerMasafumi Ogawa's paper presents challenge after challenge facing the teacher and the teacher educator in Japan. One has the sense that a lifetime of frustrations with the national curriculum, the set-up of student teaching, and the definition of music as a school subject each made its way into the paper. Even choosing to focus on teacher (...) training still leaves a very broad topic for a relatively short paper. The central challenge seems to be the curriculum. How does the curriculum impact the teacher and the teacher training process? How does the underlying definition of music as well as the purpose that definition implies affect the curriculum? His paper also identifies a series of dualities or tensions that exist between two important components: the curriculum or teacher education. The fact that Japanese and American music education systems seem to be at opposite ends of some of these dualities is a compelling reason for exploring and discussing them.In the arena of teacher preparation, the dualities as they appear in their relative proportion of the teacher education curriculum are (1) performance versus academic music courses, such as history, theory, and composition, and (2) education versus music courses—a familiar lament among music education students. In student teaching, modeling in the classroom by the cooperating teacher is contrasted with providing opportunities for the student teacher to experiment with the teaching process. Evaluation of student teaching is a three-way tension involving the student teacher, the cooperating teacher, and the university professor.In his discussion of the school curriculum, Ogawa deplores the triumph of attitude over skill, and pleads for discernment in the application of national standards to meet the needs of the community and students. He returns to the nature of music and music education at several points in his paper, expanding the meaning and function of music beyond music as art. His dissatisfaction with the seemingly teacher-proof curriculum peaks when he advocates for the autonomy of the teacher in the classroom. Giving teachers the opportunity to devise their own curriculum seems to go to the other extreme. Having taught with colleagues who had virtually no training in music, a standard curriculum at the district or national level provides some essential boundaries.Ogawa's discussion of the impact of the national Course of Study on Japanese music education was particularly intriguing. As teacher certification in the United [End Page 205] States has begun to promote and reward National Board Certification, it is striking to consider the restrictions and disempowerment that Ogawa describes and credits to the omnipresent Course of Study. For someone unfamiliar with the Japanese system of education, some of the descriptions were enticing but brief. Other descriptions were a bit confusing, but after visiting the MEXT website, I think most of this confusion is due to translation. It is difficult to take any phrase that is packed with meaning in one culture and find a suitable phrase in another culture that will convey the associations that are connected with it. I would recommend quoting complete descriptions or including an appendix. A reference to the history of Japanese music education on Kensho Takeshi's website would also provide more context, particularly for the connection between emotion, music, and ethics.I want to thank Ogawa for stimulating me to consider issues of curriculum including how I have changed my views of curriculum since I returned to school teaching. First, I will describe my change of perspective. Then I would like to close by describing an aspect of curriculum and teacher education that has surfaced this past year. I would call this the meta-curriculum, and I wonder how we can prepare new teachers for this part of teaching. It seems to me that the world of philosophy is the quintessential and perhaps the only appropriate arena for this preparation.Beyond Curriculum in the ClassroomLike the first spring rain on newly cut grass, music education has a fresh and vital look to me. I returned to public school teaching this year after a hiatus of seventeen years. After focusing on viola performance and liberal arts... (shrink)

Two compelling principles, the Reasonable Range Principle and the Preservation of Irrelevant Evidence Principle, are necessary conditions that any response to peer disagreements ought to abide by. The Reasonable Range Principle maintains that a resolution to a peer disagreement should not fall outside the range of views expressed by the peers in their dispute, whereas the Preservation of Irrelevant Evidence Principle maintains that a resolution strategy should be able to preserve unanimous judgments of evidential irrelevance among the peers. No standard (...) Bayesian resolution strategy satisfies the PIE Principle, however, and we give a loss aversion argument in support of PIE and against Bayes. The theory of imprecise probability allows one to satisfy both principles, and we introduce the notion of a set-based credal judgment to frame and address a range of subtle issues that arise in peer disagreements. (shrink)

This impressive volume of essays that includes contributions from Herbert Dreyfus, Sean Kelly, Mike Wheeler, Dan Zahavi, and Shaun Gallagher reflects an emerging trend in cognitive science, and explores this new approach to cognitive science informed by Heidegger's thoughts on human existence.

Dilation occurs when an interval probability estimate of some event E is properly included in the interval probability estimate of E conditional on every event F of some partition, which means that one’s initial estimate of E becomes less precise no matter how an experiment turns out. Critics maintain that dilation is a pathological feature of imprecise probability models, while others have thought the problem is with Bayesian updating. However, two points are often overlooked: (1) knowing that E is stochastically (...) independent of F (for all F in a partition of the underlying state space) is sufficient to avoid dilation, but (2) stochastic independence is not the only independence concept at play within imprecise probability models. In this paper we give a simple characterization of dilation formulated in terms of deviation from stochastic independence, propose a measure of dilation, and distinguish between proper and improper dilation. Through this we revisit the most sensational examples of dilation, which play up independence between dilator and dilatee, and find the sensationalism undermined by either fallacious reasoning with imprecise probabilities or improperly constructed imprecise probability models. (shrink)

Prominent evolutionary psychologists have argued that our innate psychological endowment consists of numerous domain‐specific cognitive resources, rather than a few domain‐general ones. In the light of some conceptual clarification, we examine the central in‐principle arguments that evolutionary psychologists mount against domain‐general cognition. We conclude (a) that the fundamental logic of Darwinism, as advanced within evolutionary psychology, does not entail that the innate mind consists exclusively, or even massively, of domain‐specific features, and (b) that a mixed innate cognitive economy of domain‐specific (...) and domain‐general resources remains a genuine conceptual possibility. However, an examination of evolutionary psychology's ‘grain problem’ reveals that there is no way of establishing a principled and robust distinction between domain‐specific and domain‐general features. Nevertheless, we show that evolutionary psychologists can and do live with this grain problem without their whole enterprise being undermined. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are (...) rarely correctly identified as such in lower-dimensional representations if random projections are used. In such projections, the expected curvature in a lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature and mean curvature (i.e., the normalized Hessian trace) to estimate the trace of Hessians without calculating the Hessian or Hessian-vector products as in Hutchinson’s method. Because random projections are not able to correctly identify saddle information, we propose to study projections along Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, we illustrate our method in numerical experiments on different image classifiers with up to about 7 × 10^6 parameters. (shrink)

Prominent evolutionary psychologists have argued that our innate psychological endowment consists of numerous domainspecific cognitive resources, rather than a few domaingeneral ones. In the light of some conceptual clarification, we examine the central inprinciple arguments that evolutionary psychologists mount against domaingeneral cognition. We conclude (a) that the fundamental logic of Darwinism, as advanced within evolutionary psychology, does not entail that the innate mind consists exclusively, or even massively, of domainspecific features, and (b) that a mixed innate cognitive economy of domainspecific (...) and domaingeneral resources remains a genuine conceptual possibility. However, an examination of evolutionary psychology's 'grain problem' reveals that there is no way of establishing a principled and robust distinction between domainspecific and domaingeneral features. Nevertheless, we show that evolutionary psychologists can and do live with this grain problem without their whole enterprise being undermined. (shrink)

Samuel C. Wheeler, III; The Extension of Deconstruction, The Monist, Volume 69, Issue 1, 1 January 1986, Pages 3–21, https://doi.org/10.5840/monist19866913.

In this paper, we present a new semantic challenge to the moral error theory. Its first component calls upon moral error theorists to deliver a deontic semantics that is consistent with the error-theoretic denial of moral truths by returning the truth-value false to all moral deontic sentences. We call this the ‘consistency challenge’ to the moral error theory. Its second component demands that error theorists explain in which way moral deontic assertions can be seen to differ in meaning despite necessarily (...) sharing the same intension. We call this the ‘triviality challenge’ to the moral error theory. Error theorists can either meet the consistency challenge or the triviality challenge, we argue, but are hard pressed to meet both. (shrink)

Recent debate about the error theory has taken a ‘formal turn’. On the one hand, there are those who argue that the error theory should be rejected because of its difficulties in providing a convincing formal account of the logic and semantics of moral claims. On the other hand, there are those who claim that such formal objections fail, maintaining that arguments against the error theory must be of a substantive rather than a formal kind. In this paper, we argue (...) that formal objections to the error theory cannot be eschewed but must be met head-on. (shrink)

Analyzing geometric properties of high-dimensional loss functions, such as local curvature and the existence of other optima around a certain point in loss space, can help provide a better understanding of the interplay between neural network structure, implementation attributes, and learning performance. In this work, we combine concepts from high-dimensional probability and differential geometry to study how curvature properties in lower-dimensional loss representations depend on those in the original loss space. We show that saddle points in the original space are (...) rarely correctly identified as such in expected lower-dimensional representations if random projections are used. The principal curvature in the expected lower-dimensional representation is proportional to the mean curvature in the original loss space. Hence, the mean curvature in the original loss space determines if saddle points appear, on average, as either minima, maxima, or almost flat regions. We use the connection between expected curvature in random projections and mean curvature in the original space (i.e., the normalized Hessian trace) to compute Hutchinson-type trace estimates without calculating Hessian-vector products as in the original Hutchinson method. Because random projections are not suitable to correctly identify saddle information, we propose to study projections along dominant Hessian directions that are associated with the largest and smallest principal curvatures. We connect our findings to the ongoing debate on loss landscape flatness and generalizability. Finally, for different common image classifiers and a function approximator, we show and compare random and Hessian projections of loss landscapes with up to about 7×10^6 parameters. (shrink)